Behavioral Data

Demographics

First, let’s load the data and transform it into a Wide format table

behav <- read_tsv("data/behav/behav_data.txt",
                  col_types=cols())

behav$material[behav$material=="Swahili"] <- "Vocabulary"
behav$material[behav$material=="US Maps"] <- "Maps"

behav <- behav %>% rename(Gender = gender, Age = age)

wbehav <- behav %>% pivot_wider(values_from = alpha,
                                id_cols = c(Subject, Gender, Age),
                                names_from = material)

At this point, we can look at the participant demographocs

ggplot(data=wbehav, aes(x=Age, col=Gender)) +
  geom_histogram(aes(col="white", fill=Gender),
                 colour="white", alpha=0.5, 
                 position="identity", binwidth = 1) +
  scale_color_brewer(palette = "Set1") +
  scale_fill_brewer(palette = "Set1") +
  ggtitle("Age Distribution by Gender") + 
  theme_pander()
## Warning: Removed 2 rows containing non-finite values (stat_bin).

Rate of Forgetting (Alpha parameter) for the two tasks

We can now examine the distribution and correlation of the rate of forgetting for the verbal (Vocabulary) and Maps:

mu <- behav %>% 
  group_by(material) %>% 
  summarize(alpha=mean(alpha))
## `summarise()` ungrouping output (override with `.groups` argument)
p1 <- ggplot(behav, aes(x=alpha, fill=material)) +
  geom_histogram(col="white", binwidth = 0.025, 
                 alpha=0.5, position="identity") +
  scale_color_brewer(palette = "Dark2") +
  scale_fill_brewer(palette = "Dark2") +
  geom_vline(data=mu, aes(xintercept=alpha, color=material),
             linetype="dashed") +
  xlab(expression(paste("Estimated value of ", alpha))) +
  theme_pander() +
  ylab("Count") +
  ggtitle("(A) Distribution By Materials") +
  theme(legend.position = c(0.2, 0.8)) +
  theme(plot.title = element_text(hjust = 0.5))

p2 <- ggplot(wbehav, aes(x=Vocabulary, y=Maps)) +
  geom_point(size=4, alpha=0.5, col="black") + #col=K[7]) +
  geom_smooth(method = "lm", formula = y ~ x, 
              col="red", fill="red", fullrange = T, lwd=2) +
  theme_pander() +
  scale_x_continuous() + 
  scale_y_continuous() + 
  ggtitle("(B) Correlation Across Materials") +
  xlab(expression(paste(alpha, " Vocabulary"))) +
  ylab(expression(paste(alpha, " Maps"))) +
  geom_rug(col="black", lwd=1, alpha=.5) +
  annotate("segment", x=0.1, y=0.1, xend=0.5, 
           yend=0.5, col="grey", lwd=1, lty=2) +
  theme(plot.title = element_text(hjust = 0.5))
  
grid.arrange(p1, p2, ncol=2)

p3 <- ggplot(wbehav, aes(x=Vocabulary, y=Maps)) +
  geom_point(size=4, alpha=0.5, col="black") + #col=K[7]) +
  geom_smooth(method = "lm", formula = y ~ x, col="red", 
              fill="red", fullrange = T, lwd=2) +
  theme_pander() +
  scale_x_continuous() + 
  scale_y_continuous() + 
  coord_fixed() +
  ggtitle("Correlation of Alpha Parameters\nAcross Materials") +
  xlab(expression(paste(alpha, " Vocabulary"))) +
  ylab(expression(paste(alpha, " Maps"))) +
  annotate("segment", x=0.1, y=0.1, xend=0.5, 
           yend=0.5, col="grey", lwd=1, lty=2) +
  annotate("text", label = paste("R =", round(cor(wbehav$Vocabulary,
                                                  wbehav$Maps),
                                              2)), 
                                 x=0.2, y=0.45, col="red") +
  
  theme(plot.title = element_text(hjust = 0.5))

ggMarginal(p3, col="white", fill="black", alpha=0.5,
           type="hist", bins=13)

And here is a summary of the data:

summary(wbehav) %>%
  xtable() %>%
  kable(digits = 3) %>%
  kable_styling(bootstrap_options = c("striped", "hover"))
Subject Gender Age Vocabulary Maps
X Length:50 Length:50 Min. :18.00 Min. :0.1219 Min. :0.2120
X.1 Class :character Class :character 1st Qu.:18.00 1st Qu.:0.2647 1st Qu.:0.3039
X.2 Mode :character Mode :character Median :19.00 Median :0.2917 Median :0.3447
X.3 NA NA Mean :18.92 Mean :0.2825 Mean :0.3355
X.4 NA NA 3rd Qu.:19.00 3rd Qu.:0.3203 3rd Qu.:0.3680
X.5 NA NA Max. :22.00 Max. :0.3852 Max. :0.4701
X.6 NA NA NA’s :2 NA NA

Eyes-Closed EEG Data

Now we look at the neural correlates of the rates of forgetting in EEG data. We begin with eyes closed EEG data, which is the most common type of resting-state EEG recording.

(Optional) Preprocess the Data

Set the process_raw variable to TRUE to reprocess the raw EEG data. That might take a very long time.

process_raw = F
if (process_raw) {
  setwd("./data/eyes_closed/")
  for (sub in dir(grep("A[1-9]", dir()))) {
    setwd(sub)
    analyze.logfile(sub, "closed")
    setwd("..")
  }
  setwd("../..")
}

Load the Eyes-Closed Spectra and Summary Files

The preprocessing step produces a number of text files. Here, we are interested in the summary file, which contains many useful statistics, including the Individual Alpha Frequency (i.e., the Alpha Peak) for each channel, the spectra file, which contains the estimated log power for each channel in increments of 0.5 Hz.

ec_spectra <- NULL
for (sub in dir("data/eyes_closed/")[grep("A[1-9]",
                                        dir("data/eyes_closed/"))]) {
  table <- read_tsv(paste("data/eyes_closed/", sub, "/", 
                          sub, "_closed_spectra.txt", sep=""),
                    col_types = cols())
  if (is.null(ec_spectra)) {
    ec_spectra <- table
  } else {
    ec_spectra <- ec_spectra %>% bind_rows(table)
  }
}

ec_summary <- NULL
for (sub in dir("data/eyes_closed/")[grep("A[1-9]", 
                                          dir("data/eyes_closed/"))]) {
  table <- read_tsv(paste("data/eyes_closed/", sub, "/", 
                          sub, "_closed_summary.txt", sep=""),
                    col_types = cols())
  if (is.null(ec_summary)) {
    ec_summary <- table
  } else {
    ec_summary <- ec_summary %>% bind_rows(table)
  }
}

Individual Alpha frquency

The IAF is perhaps the most important subject level characteristic of the resting state spectrum. For this reason, we want to get some basic statistics. First, we calculate the subject-level IAF by computing the mode IAF across all channels for a given participant.

iaf_cols <- paste(c("AF3", "AF4", "F3", "F4", 
                    "F7", "F8", "FC5", "FC6", 
                    "T7", "T8", "P7", "P8", 
                    "O1", "O2"), 
                  "IAF", 
                  sep="_")

ec_iafs <- ec_summary %>%
  select(c("Subject", iaf_cols)) %>%
  filter(Subject %in% wbehav$Subject) %>%
  pivot_longer(cols = iaf_cols, names_sep="_", 
               names_to = c("Channel", "Discard"), 
               values_to = "IAF_EC") %>%
  select(Subject, Channel, IAF_EC) %>%
  group_by(Subject) %>%
  summarize(IAF_EC = Mode(IAF_EC))
## Note: Using an external vector in selections is ambiguous.
## ℹ Use `all_of(iaf_cols)` instead of `iaf_cols` to silence this message.
## ℹ See <https://tidyselect.r-lib.org/reference/faq-external-vector.html>.
## This message is displayed once per session.
## `summarise()` ungrouping output (override with `.groups` argument)

The mean IAF thus calculated is 10.3, which is exactly in the middle of our alpha frequency band.

ggplot(data=ec_iafs, aes(x = IAF_EC)) +
  geom_histogram(aes(col="white"), fill="black", 
                 colour="white", alpha=0.5, 
                 position="identity", binwidth = 0.5) +
  ggtitle("IAF Distribution, Eyes Closed") + 
  xlab("IAF (Eyes Closed)") +
  theme_pander()

Average Spectrum

First, let’s examine the spectrograms for each channel to make sure it looks normal and the IAF (individual alpha frequency) is reasonable, i.e., the same for each channel and roughly in the middle of the band definition

l_ec_spectra <- pivot_longer(ec_spectra, cols=names(ec_spectra)[3:130], 
                         names_to="Freq")

l_ec_spectra <- l_ec_spectra %>% 
  rename(Power = value) %>%
  add_column(Recording = "Eyes Closed")

l_ec_spectra$Frequency <- as.numeric(substr(l_ec_spectra$Freq, 
                                            0, str_length(l_ec_spectra$Freq) -2))
l_ec_spectra <- l_ec_spectra %>% 
  add_column(Band="Delta", BandMin=0, BandMax=4) 
l_ec_spectra$Band[l_ec_spectra$Frequency <= 40] <- "Gamma"
l_ec_spectra$Band[l_ec_spectra$Frequency < 30] <- "High Beta"
l_ec_spectra$Band[l_ec_spectra$Frequency < 18] <- "Upper Beta"
l_ec_spectra$Band[l_ec_spectra$Frequency < 15] <- "Low Beta"
l_ec_spectra$Band[l_ec_spectra$Frequency < 13] <- "Alpha"
l_ec_spectra$Band[l_ec_spectra$Frequency < 8] <- "Theta"
l_ec_spectra$Band[l_ec_spectra$Frequency < 4] <- "Delta"

l_ec_spectra$BandMin[l_ec_spectra$Frequency <= 40] <- 30
l_ec_spectra$BandMin[l_ec_spectra$Frequency < 30] <- 18
l_ec_spectra$BandMin[l_ec_spectra$Frequency < 18] <- 15
l_ec_spectra$BandMin[l_ec_spectra$Frequency < 15] <- 13
l_ec_spectra$BandMin[l_ec_spectra$Frequency < 13] <- 8
l_ec_spectra$BandMin[l_ec_spectra$Frequency < 8] <- 4
l_ec_spectra$BandMin[l_ec_spectra$Frequency < 4] <- 0

l_ec_spectra$BandMax[l_ec_spectra$Frequency <= 40] <- 40
l_ec_spectra$BandMax[l_ec_spectra$Frequency < 30] <- 30
l_ec_spectra$BandMax[l_ec_spectra$Frequency < 18] <- 18
l_ec_spectra$BandMax[l_ec_spectra$Frequency < 15] <- 15
l_ec_spectra$BandMax[l_ec_spectra$Frequency < 13] <- 13
l_ec_spectra$BandMax[l_ec_spectra$Frequency < 8] <- 8
l_ec_spectra$BandMax[l_ec_spectra$Frequency < 4] <- 4

l_ec_spectra$Band <- factor(l_ec_spectra$Band, 
                        levels = c("Delta", "Theta", "Alpha", 
                                   "Low Beta", "Upper Beta",
                                   "High Beta", "Gamma"))

Now, we remove the three participants for which we have poor quality data

l_ec_spectra <- l_ec_spectra %>%
  filter(Subject %in% behav$Subject)

We can visualize the power spectra to ensure that our data looks normal

gd <- l_ec_spectra %>% 
        group_by(Band) %>% 
        summarise(
          Min = mean(BandMin),
          Max = mean(BandMax),
          Power =mean(Power),
          Frequency = mean(BandMin)
          #Channel=
        )
## `summarise()` ungrouping output (override with `.groups` argument)
ggplot(data=l_ec_spectra, aes(x=Frequency, y=Power, Channel)) +
  geom_rect(data = gd, aes(xmin = Min, xmax = Max, fill = Band), 
            ymin=0, ymax=Inf, colour=NA, alpha=0.5) +
  stat_summary(fun.data=mean_sdl, 
               geom = "ribbon", colour = "white", alpha = 0.4) +
  stat_summary(fun = mean, geom = "line", lwd = 1) +
  facet_wrap(~ Channel, ncol=4) +
  scale_alpha_manual(values = seq(0.1, 0.9, 0.1)) +
  ggtitle("Eyes-Closed Power Spectrum Across Channels") +
  ylab("Log Power") + 
  xlab("Frequency (Hz)") + 
  theme_pander() +
  coord_cartesian(xlim=c(1,40), ylim=c(5, 17)) + #ylim=c(5,17)) +
  scale_fill_brewer(palette = "Set3") +
  theme(plot.title = element_text(hjust = 0.5))

Now, let’s create a mean spectrogram with annotations that mark the different frequency bands. It serves as a visual reference that our data is not grossly out of whack.

K = brewer.pal(7, "Set3")

al_ec_spectra <- aggregate(l_ec_spectra[c("Power")],
                       list(Subject = l_ec_spectra$Subject, 
                            Frequency = l_ec_spectra$Frequency, 
                            Band = l_ec_spectra$Band), 
                       mean)

ggplot(data=al_ec_spectra, aes(x=Frequency, y=Power, col=Power)) +
  annotate("rect", xmin = 0, xmax = 4, ymin = 0, ymax = Inf, 
           alpha = 0.5, fill=K[1]) +
  annotate("rect", xmin = 4, xmax = 8, ymin = 0, ymax = Inf, 
           alpha = 0.5, fill=K[2]) +
  annotate("rect", xmin = 8, xmax = 13, ymin = 0, ymax = Inf, 
           alpha = 0.5, fill=K[3]) +      
  annotate("rect", xmin = 13, xmax = 15, ymin = 0, ymax = Inf, 
           alpha = 0.5, fill=K[4]) +
  annotate("rect", xmin = 15, xmax = 18, ymin = 0, ymax = Inf, 
           alpha = 0.5, fill = K[5]) +
  annotate("rect", xmin = 18, xmax = 30, ymin = 0, ymax = Inf, 
           alpha = 0.5, fill=K[6]) +
  annotate("rect", xmin = 30, xmax = 40, ymin = 0, ymax = Inf,
           alpha = 0.5, fill=K[7]) +
  stat_summary(fun.data = mean_sdl, geom = "ribbon", 
               alpha = 0.5, fill = "grey50", col = "white") +
  stat_summary(fun=mean, geom="line", lwd=2) +
  coord_cartesian(xlim=c(0,40), ylim=c(5,18)) +
  xlab("Frequency (Hz)") +
  theme_pander() +
  annotate("text", x=2, y=5, label="Delta", angle=90, hjust=0) +
  annotate("text", x=6, y=5, label="Theta", angle=90, hjust=0) +
  annotate("text", x=10.5, y=5, label="Alpha", angle=90, hjust=0) +
  annotate("text", x=14, y=5, label="Low Beta", angle=90, hjust=0) +
  annotate("text", x=16.5, y=5, label="Upper Beta", angle=90, hjust=0) +
  annotate("text", x=24, y=5, label="High Beta", angle=90, hjust=0) +
  annotate("text", x=35, y=5, label="Gamma", angle=90, hjust=0)

Correlations with Rate of Forgetting

Having ensured that our EEG recordings look normal, reflect known neurophysiological characteristics, and that our frequency bands boundaries are reasonable, we can proceed with correlating the rates of forgetting with resting state QEEG characteristics.

First, we calculate the mean power for every band and channel, remove participants who were not included in the behavioral tests, and correct for multiple comparisons by frequency band:

r2p <- function(r, n) {
  df = n - 2
  t = (r * sqrt(df)) / sqrt(1 - r**2)
  2 * pt(-abs(t), df = df)
}

wbehav <- wbehav %>%
  mutate(GlobalAlpha=(Vocabulary + Maps)/2)

Adata_ec <- l_ec_spectra %>% 
  group_by(Subject, Channel, Band, Recording) %>% 
  summarize(Power=mean(Power))
## `summarise()` regrouping output by 'Subject', 'Channel', 'Band' (override with `.groups` argument)
Fdata_ec <- inner_join(Adata_ec, behav, by="Subject")

Rdata_ec <- Fdata_ec %>%
  group_by(material, Channel, Band, Recording) %>%
  summarise(r = cor(Power, alpha),
            rob_r =robcor(Power, alpha, method="ssd"),
            p = cor.test(Power, alpha)$p.value)
## `summarise()` regrouping output by 'material', 'Channel', 'Band' (override with `.groups` argument)
Rdata_ec <- Rdata_ec %>%
  group_by(material, Band, Recording) %>%
  mutate(q = p.adjust(p, method="BH"),
         rob_p = r2p(rob_r, n=50))  %>%
  mutate(rob_q = p.adjust(rob_p, method="BH"))

Here is the full table of statistics:

write_csv(Rdata_ec, "correlations_channel_band_eyes_closed.csv", col_names = T)

Rdata_ec %>%
  xtable() %>%
  kable(digits = 3) %>%
  kable_styling(bootstrap_options = c("striped", "hover"))
material Channel Band Recording r rob_r p q rob_p rob_q
Maps AF3 Delta Eyes Closed 0.010 -0.132 0.947 0.971 0.360 0.722
Maps AF3 Theta Eyes Closed 0.072 -0.060 0.621 0.790 0.681 0.953
Maps AF3 Alpha Eyes Closed 0.113 0.104 0.436 0.592 0.474 0.830
Maps AF3 Low Beta Eyes Closed 0.189 0.155 0.188 0.316 0.282 0.497
Maps AF3 Upper Beta Eyes Closed 0.314 0.262 0.026 0.092 0.066 0.184
Maps AF3 High Beta Eyes Closed 0.219 0.153 0.127 0.403 0.287 0.647
Maps AF3 Gamma Eyes Closed 0.101 -0.072 0.484 0.924 0.617 0.963
Maps AF4 Delta Eyes Closed 0.096 -0.008 0.507 0.971 0.955 0.969
Maps AF4 Theta Eyes Closed 0.079 -0.008 0.585 0.790 0.958 0.976
Maps AF4 Alpha Eyes Closed 0.147 0.128 0.308 0.582 0.374 0.760
Maps AF4 Low Beta Eyes Closed 0.216 0.199 0.132 0.316 0.166 0.497
Maps AF4 Upper Beta Eyes Closed 0.339 0.325 0.016 0.092 0.021 0.184
Maps AF4 High Beta Eyes Closed 0.280 0.219 0.049 0.342 0.126 0.647
Maps AF4 Gamma Eyes Closed 0.145 -0.007 0.315 0.924 0.963 0.963
Maps F3 Delta Eyes Closed -0.005 -0.047 0.971 0.971 0.747 0.928
Maps F3 Theta Eyes Closed 0.072 0.004 0.619 0.790 0.976 0.976
Maps F3 Alpha Eyes Closed 0.140 0.089 0.333 0.582 0.540 0.839
Maps F3 Low Beta Eyes Closed 0.183 0.106 0.203 0.316 0.462 0.497
Maps F3 Upper Beta Eyes Closed 0.256 0.175 0.073 0.120 0.225 0.393
Maps F3 High Beta Eyes Closed 0.184 0.135 0.200 0.403 0.349 0.647
Maps F3 Gamma Eyes Closed 0.022 0.015 0.881 0.924 0.919 0.963
Maps F4 Delta Eyes Closed 0.239 0.223 0.095 0.343 0.119 0.518
Maps F4 Theta Eyes Closed 0.122 0.159 0.400 0.790 0.271 0.773
Maps F4 Alpha Eyes Closed 0.156 0.127 0.278 0.582 0.380 0.760
Maps F4 Low Beta Eyes Closed 0.200 0.184 0.164 0.316 0.202 0.497
Maps F4 Upper Beta Eyes Closed 0.290 0.265 0.041 0.116 0.063 0.184
Maps F4 High Beta Eyes Closed 0.215 0.217 0.133 0.403 0.130 0.647
Maps F4 Gamma Eyes Closed 0.135 0.099 0.349 0.924 0.493 0.963
Maps F7 Delta Eyes Closed -0.058 -0.074 0.689 0.971 0.609 0.928
Maps F7 Theta Eyes Closed 0.087 -0.026 0.550 0.790 0.860 0.976
Maps F7 Alpha Eyes Closed 0.115 0.040 0.425 0.592 0.783 0.844
Maps F7 Low Beta Eyes Closed 0.203 0.113 0.158 0.316 0.435 0.497
Maps F7 Upper Beta Eyes Closed 0.254 0.149 0.075 0.120 0.301 0.468
Maps F7 High Beta Eyes Closed 0.121 -0.111 0.403 0.564 0.441 0.647
Maps F7 Gamma Eyes Closed -0.021 -0.191 0.885 0.924 0.183 0.918
Maps F8 Delta Eyes Closed 0.011 -0.038 0.939 0.971 0.795 0.928
Maps F8 Theta Eyes Closed 0.147 0.157 0.309 0.790 0.276 0.773
Maps F8 Alpha Eyes Closed 0.173 0.158 0.230 0.582 0.272 0.760
Maps F8 Low Beta Eyes Closed 0.206 0.209 0.152 0.316 0.146 0.497
Maps F8 Upper Beta Eyes Closed 0.319 0.282 0.024 0.092 0.048 0.184
Maps F8 High Beta Eyes Closed 0.184 0.114 0.201 0.403 0.432 0.647
Maps F8 Gamma Eyes Closed 0.065 -0.050 0.655 0.924 0.729 0.963
Maps FC5 Delta Eyes Closed -0.030 -0.041 0.838 0.971 0.776 0.928
Maps FC5 Theta Eyes Closed 0.025 -0.093 0.865 0.932 0.520 0.953
Maps FC5 Alpha Eyes Closed 0.078 -0.017 0.591 0.637 0.906 0.906
Maps FC5 Low Beta Eyes Closed 0.128 0.107 0.376 0.526 0.460 0.497
Maps FC5 Upper Beta Eyes Closed 0.153 0.079 0.288 0.367 0.587 0.632
Maps FC5 High Beta Eyes Closed 0.071 0.053 0.622 0.725 0.714 0.752
Maps FC5 Gamma Eyes Closed 0.014 0.026 0.924 0.924 0.855 0.963
Maps FC6 Delta Eyes Closed 0.069 0.006 0.633 0.971 0.969 0.969
Maps FC6 Theta Eyes Closed 0.106 0.106 0.462 0.790 0.464 0.953
Maps FC6 Alpha Eyes Closed 0.167 0.149 0.247 0.582 0.302 0.760
Maps FC6 Low Beta Eyes Closed 0.183 0.202 0.203 0.316 0.159 0.497
Maps FC6 Upper Beta Eyes Closed 0.272 0.296 0.056 0.120 0.037 0.184
Maps FC6 High Beta Eyes Closed 0.153 0.097 0.290 0.507 0.501 0.647
Maps FC6 Gamma Eyes Closed 0.088 -0.050 0.545 0.924 0.733 0.963
Maps O1 Delta Eyes Closed 0.221 0.132 0.123 0.343 0.361 0.722
Maps O1 Theta Eyes Closed 0.009 0.027 0.952 0.952 0.851 0.976
Maps O1 Alpha Eyes Closed -0.096 -0.041 0.508 0.592 0.775 0.844
Maps O1 Low Beta Eyes Closed -0.039 -0.110 0.786 0.847 0.446 0.497
Maps O1 Upper Beta Eyes Closed 0.100 -0.029 0.491 0.573 0.844 0.844
Maps O1 High Beta Eyes Closed 0.093 0.046 0.519 0.660 0.752 0.752
Maps O1 Gamma Eyes Closed 0.139 0.170 0.336 0.924 0.237 0.918
Maps O2 Delta Eyes Closed 0.229 0.191 0.109 0.343 0.185 0.518
Maps O2 Theta Eyes Closed 0.106 0.073 0.463 0.790 0.615 0.953
Maps O2 Alpha Eyes Closed 0.060 0.075 0.680 0.680 0.605 0.844
Maps O2 Low Beta Eyes Closed 0.098 0.117 0.497 0.632 0.419 0.497
Maps O2 Upper Beta Eyes Closed 0.193 0.118 0.180 0.252 0.415 0.582
Maps O2 High Beta Eyes Closed 0.205 0.172 0.153 0.403 0.233 0.647
Maps O2 Gamma Eyes Closed 0.181 0.225 0.209 0.924 0.116 0.918
Maps P7 Delta Eyes Closed 0.201 0.094 0.161 0.375 0.516 0.903
Maps P7 Theta Eyes Closed -0.037 0.066 0.798 0.931 0.651 0.953
Maps P7 Alpha Eyes Closed -0.148 0.056 0.306 0.582 0.697 0.844
Maps P7 Low Beta Eyes Closed -0.028 -0.012 0.847 0.847 0.933 0.933
Maps P7 Upper Beta Eyes Closed 0.049 0.094 0.735 0.791 0.516 0.617
Maps P7 High Beta Eyes Closed 0.027 0.069 0.852 0.852 0.634 0.740
Maps P7 Gamma Eyes Closed 0.028 0.136 0.846 0.924 0.346 0.963
Maps P8 Delta Eyes Closed 0.326 0.201 0.021 0.290 0.162 0.518
Maps P8 Theta Eyes Closed 0.343 0.192 0.015 0.208 0.181 0.773
Maps P8 Alpha Eyes Closed 0.222 0.171 0.122 0.582 0.236 0.760
Maps P8 Low Beta Eyes Closed 0.298 0.223 0.036 0.316 0.120 0.497
Maps P8 Upper Beta Eyes Closed 0.365 0.196 0.009 0.092 0.171 0.343
Maps P8 High Beta Eyes Closed 0.332 0.115 0.018 0.258 0.427 0.647
Maps P8 Gamma Eyes Closed 0.288 0.162 0.043 0.599 0.262 0.918
Maps T7 Delta Eyes Closed -0.042 -0.245 0.770 0.971 0.086 0.518
Maps T7 Theta Eyes Closed -0.148 -0.196 0.307 0.790 0.172 0.773
Maps T7 Alpha Eyes Closed -0.099 -0.184 0.494 0.592 0.200 0.760
Maps T7 Low Beta Eyes Closed -0.060 -0.137 0.681 0.795 0.343 0.497
Maps T7 Upper Beta Eyes Closed -0.023 -0.091 0.876 0.876 0.529 0.617
Maps T7 High Beta Eyes Closed -0.037 -0.183 0.797 0.852 0.203 0.647
Maps T7 Gamma Eyes Closed -0.017 -0.106 0.905 0.924 0.463 0.963
Maps T8 Delta Eyes Closed 0.247 0.310 0.084 0.343 0.028 0.397
Maps T8 Theta Eyes Closed 0.251 0.291 0.078 0.547 0.041 0.570
Maps T8 Alpha Eyes Closed 0.239 0.227 0.095 0.582 0.113 0.760
Maps T8 Low Beta Eyes Closed 0.214 0.177 0.135 0.316 0.218 0.497
Maps T8 Upper Beta Eyes Closed 0.252 0.217 0.077 0.120 0.130 0.303
Maps T8 High Beta Eyes Closed 0.140 0.096 0.332 0.517 0.508 0.647
Maps T8 Gamma Eyes Closed 0.036 -0.007 0.804 0.924 0.962 0.963
Vocabulary AF3 Delta Eyes Closed -0.008 -0.149 0.958 0.958 0.303 0.707
Vocabulary AF3 Theta Eyes Closed 0.023 -0.040 0.873 0.962 0.784 0.989
Vocabulary AF3 Alpha Eyes Closed 0.086 -0.016 0.553 0.779 0.914 0.934
Vocabulary AF3 Low Beta Eyes Closed 0.298 0.181 0.035 0.145 0.208 0.450
Vocabulary AF3 Upper Beta Eyes Closed 0.225 0.126 0.116 0.334 0.385 0.794
Vocabulary AF3 High Beta Eyes Closed 0.020 -0.046 0.890 0.958 0.753 0.832
Vocabulary AF3 Gamma Eyes Closed -0.091 -0.155 0.529 0.617 0.281 0.662
Vocabulary AF4 Delta Eyes Closed -0.059 -0.176 0.683 0.939 0.221 0.707
Vocabulary AF4 Theta Eyes Closed 0.036 -0.030 0.802 0.962 0.838 0.989
Vocabulary AF4 Alpha Eyes Closed 0.105 0.040 0.466 0.779 0.783 0.934
Vocabulary AF4 Low Beta Eyes Closed 0.257 0.144 0.071 0.157 0.319 0.450
Vocabulary AF4 Upper Beta Eyes Closed 0.223 0.114 0.119 0.334 0.430 0.794
Vocabulary AF4 High Beta Eyes Closed 0.026 -0.089 0.859 0.958 0.537 0.832
Vocabulary AF4 Gamma Eyes Closed -0.114 -0.142 0.432 0.605 0.324 0.662
Vocabulary F3 Delta Eyes Closed -0.201 -0.230 0.162 0.939 0.108 0.707
Vocabulary F3 Theta Eyes Closed -0.007 -0.008 0.962 0.962 0.956 0.989
Vocabulary F3 Alpha Eyes Closed 0.064 0.020 0.660 0.840 0.891 0.934
Vocabulary F3 Low Beta Eyes Closed 0.235 0.209 0.101 0.157 0.145 0.450
Vocabulary F3 Upper Beta Eyes Closed 0.175 0.029 0.223 0.428 0.840 0.900
Vocabulary F3 High Beta Eyes Closed -0.035 -0.027 0.808 0.958 0.853 0.853
Vocabulary F3 Gamma Eyes Closed -0.191 -0.028 0.185 0.581 0.847 0.894
Vocabulary F4 Delta Eyes Closed -0.041 -0.061 0.778 0.939 0.674 0.875
Vocabulary F4 Theta Eyes Closed 0.036 0.011 0.802 0.962 0.938 0.989
Vocabulary F4 Alpha Eyes Closed 0.105 0.060 0.469 0.779 0.680 0.934
Vocabulary F4 Low Beta Eyes Closed 0.273 0.162 0.055 0.154 0.261 0.450
Vocabulary F4 Upper Beta Eyes Closed 0.249 0.119 0.082 0.334 0.412 0.794
Vocabulary F4 High Beta Eyes Closed -0.001 -0.054 0.997 0.997 0.709 0.832
Vocabulary F4 Gamma Eyes Closed -0.140 -0.019 0.332 0.581 0.894 0.894
Vocabulary F7 Delta Eyes Closed 0.015 -0.023 0.917 0.958 0.875 0.875
Vocabulary F7 Theta Eyes Closed 0.029 0.046 0.842 0.962 0.753 0.989
Vocabulary F7 Alpha Eyes Closed 0.099 0.019 0.494 0.779 0.893 0.934
Vocabulary F7 Low Beta Eyes Closed 0.290 0.230 0.041 0.145 0.108 0.450
Vocabulary F7 Upper Beta Eyes Closed 0.168 0.113 0.245 0.428 0.433 0.794
Vocabulary F7 High Beta Eyes Closed -0.043 -0.069 0.765 0.958 0.634 0.832
Vocabulary F7 Gamma Eyes Closed -0.126 -0.160 0.383 0.595 0.268 0.662
Vocabulary F8 Delta Eyes Closed -0.126 -0.115 0.383 0.939 0.426 0.852
Vocabulary F8 Theta Eyes Closed -0.019 -0.043 0.897 0.962 0.768 0.989
Vocabulary F8 Alpha Eyes Closed 0.137 0.041 0.343 0.779 0.779 0.934
Vocabulary F8 Low Beta Eyes Closed 0.241 0.151 0.091 0.157 0.294 0.450
Vocabulary F8 Upper Beta Eyes Closed 0.196 0.100 0.173 0.403 0.490 0.794
Vocabulary F8 High Beta Eyes Closed -0.082 -0.042 0.571 0.958 0.773 0.832
Vocabulary F8 Gamma Eyes Closed -0.206 -0.167 0.151 0.581 0.246 0.662
Vocabulary FC5 Delta Eyes Closed -0.087 -0.215 0.546 0.939 0.135 0.707
Vocabulary FC5 Theta Eyes Closed -0.090 -0.189 0.532 0.962 0.189 0.989
Vocabulary FC5 Alpha Eyes Closed -0.007 -0.166 0.962 0.962 0.248 0.934
Vocabulary FC5 Low Beta Eyes Closed 0.148 0.143 0.306 0.357 0.321 0.450
Vocabulary FC5 Upper Beta Eyes Closed 0.046 -0.042 0.751 0.809 0.773 0.900
Vocabulary FC5 High Beta Eyes Closed -0.115 -0.082 0.428 0.958 0.573 0.832
Vocabulary FC5 Gamma Eyes Closed -0.150 -0.137 0.297 0.581 0.343 0.662
Vocabulary FC6 Delta Eyes Closed -0.092 -0.162 0.524 0.939 0.261 0.707
Vocabulary FC6 Theta Eyes Closed -0.040 -0.071 0.781 0.962 0.625 0.989
Vocabulary FC6 Alpha Eyes Closed 0.097 0.074 0.501 0.779 0.608 0.934
Vocabulary FC6 Low Beta Eyes Closed 0.203 0.173 0.157 0.214 0.229 0.450
Vocabulary FC6 Upper Beta Eyes Closed 0.154 0.111 0.286 0.444 0.444 0.794
Vocabulary FC6 High Beta Eyes Closed -0.084 -0.097 0.562 0.958 0.502 0.832
Vocabulary FC6 Gamma Eyes Closed -0.172 -0.094 0.232 0.581 0.517 0.695
Vocabulary O1 Delta Eyes Closed -0.044 -0.065 0.759 0.939 0.653 0.875
Vocabulary O1 Theta Eyes Closed 0.057 -0.077 0.697 0.962 0.593 0.989
Vocabulary O1 Alpha Eyes Closed 0.041 -0.051 0.776 0.866 0.726 0.934
Vocabulary O1 Low Beta Eyes Closed 0.198 0.089 0.168 0.214 0.538 0.622
Vocabulary O1 Upper Beta Eyes Closed 0.138 -0.126 0.340 0.476 0.382 0.794
Vocabulary O1 High Beta Eyes Closed -0.052 -0.279 0.722 0.958 0.050 0.698
Vocabulary O1 Gamma Eyes Closed -0.145 -0.127 0.315 0.581 0.378 0.662
Vocabulary O2 Delta Eyes Closed -0.036 -0.028 0.804 0.939 0.845 0.875
Vocabulary O2 Theta Eyes Closed 0.077 0.079 0.597 0.962 0.584 0.989
Vocabulary O2 Alpha Eyes Closed 0.122 0.024 0.399 0.779 0.869 0.934
Vocabulary O2 Low Beta Eyes Closed 0.340 0.269 0.016 0.111 0.059 0.412
Vocabulary O2 Upper Beta Eyes Closed 0.271 0.045 0.057 0.334 0.756 0.900
Vocabulary O2 High Beta Eyes Closed 0.071 -0.146 0.625 0.958 0.313 0.832
Vocabulary O2 Gamma Eyes Closed -0.092 -0.087 0.524 0.617 0.546 0.695
Vocabulary P7 Delta Eyes Closed -0.065 -0.068 0.656 0.939 0.640 0.875
Vocabulary P7 Theta Eyes Closed -0.121 -0.094 0.404 0.962 0.514 0.989
Vocabulary P7 Alpha Eyes Closed -0.085 0.012 0.556 0.779 0.934 0.934
Vocabulary P7 Low Beta Eyes Closed 0.040 -0.053 0.783 0.843 0.716 0.716
Vocabulary P7 Upper Beta Eyes Closed -0.020 -0.087 0.892 0.892 0.547 0.794
Vocabulary P7 High Beta Eyes Closed -0.119 -0.132 0.410 0.958 0.360 0.832
Vocabulary P7 Gamma Eyes Closed -0.184 -0.158 0.201 0.581 0.273 0.662
Vocabulary P8 Delta Eyes Closed 0.072 -0.034 0.620 0.939 0.813 0.875
Vocabulary P8 Theta Eyes Closed 0.226 0.097 0.115 0.962 0.503 0.989
Vocabulary P8 Alpha Eyes Closed 0.210 0.093 0.142 0.779 0.523 0.934
Vocabulary P8 Low Beta Eyes Closed 0.424 0.356 0.002 0.030 0.011 0.156
Vocabulary P8 Upper Beta Eyes Closed 0.335 0.138 0.017 0.242 0.341 0.794
Vocabulary P8 High Beta Eyes Closed 0.158 -0.117 0.273 0.958 0.417 0.832
Vocabulary P8 Gamma Eyes Closed 0.013 -0.104 0.926 0.926 0.473 0.695
Vocabulary T7 Delta Eyes Closed -0.051 -0.201 0.726 0.939 0.161 0.707
Vocabulary T7 Theta Eyes Closed -0.104 -0.252 0.471 0.962 0.077 0.989
Vocabulary T7 Alpha Eyes Closed 0.036 -0.126 0.804 0.866 0.385 0.934
Vocabulary T7 Low Beta Eyes Closed -0.027 -0.081 0.851 0.851 0.577 0.622
Vocabulary T7 Upper Beta Eyes Closed -0.059 -0.083 0.684 0.798 0.567 0.794
Vocabulary T7 High Beta Eyes Closed -0.058 -0.174 0.690 0.958 0.227 0.832
Vocabulary T7 Gamma Eyes Closed -0.064 -0.205 0.660 0.710 0.152 0.662
Vocabulary T8 Delta Eyes Closed -0.037 -0.026 0.798 0.939 0.855 0.875
Vocabulary T8 Theta Eyes Closed 0.041 0.002 0.779 0.962 0.989 0.989
Vocabulary T8 Alpha Eyes Closed 0.173 0.131 0.230 0.779 0.363 0.934
Vocabulary T8 Low Beta Eyes Closed 0.238 0.108 0.096 0.157 0.455 0.580
Vocabulary T8 Upper Beta Eyes Closed 0.097 -0.018 0.504 0.641 0.900 0.900
Vocabulary T8 High Beta Eyes Closed -0.096 -0.124 0.506 0.958 0.392 0.832
Vocabulary T8 Gamma Eyes Closed -0.225 -0.043 0.116 0.581 0.769 0.894

And here is the corresponding distributions of r and p values. The dashed lines correspond to a significant threshold of p < .05 on either a r or a p-value scale.

ggplot(Rdata_ec, aes(x = Band, y = r, col = Channel)) +
  geom_point() +
  stat_summary(fun.data = "mean_se", col="black", 
               alpha=0.5, geom = "errorbar") +
  facet_wrap(~ material) +
  ggtitle("Correlation by Frequency Band") +
  ylab("r value") +
  annotate("segment", x=-Inf, xend=Inf, y=0.28, yend = 0.28, lty=2) +
  annotate("segment", x=-Inf, xend=Inf, y=-0.28, yend = -0.28, lty=2) +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  theme_pander()

ggplot(Rdata_ec, aes(x = Band, y = p, col = Channel)) +
  geom_point() +
  stat_summary(fun.data = "mean_se", col="black", alpha=0.5, geom = "errorbar") +
  ggtitle("p-value, by Band") +
  ylab("p value") +
  facet_wrap(~ material) +
  annotate("segment", x=-Inf, xend=Inf, y=0.05, yend = 0.05, lty=2) +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  scale_y_log10() +
  theme_pander()

From the original list, we can extract only those channels that survive the FDR correction:

survivors <- Rdata_ec %>%
  filter(rob_q < 0.05 | q < 0.05)
  
survivors %>%
  xtable() %>%
  kable(digits = 3) %>%
  kable_styling(bootstrap_options = c("striped", "hover"))
material Channel Band Recording r rob_r p q rob_p rob_q
Vocabulary P8 Low Beta Eyes Closed 0.424 0.356 0.002 0.03 0.011 0.156

Only one channel P8, in one frequency band (low beta) survives FDR correction. We can plot the correlation between power in P8 and rate of forgetting to see the relationship:

focus <- Fdata_ec %>%
  filter(material == "Vocabulary", 
         Channel %in% survivors$Channel,
         Band == "Low Beta") %>%
  rename(Alpha = alpha)

p <- ggplot(focus, aes(x = Alpha, y = Power)) +
  geom_point(size = 4, alpha = 0.5, col = "black") + 
  geom_smooth(method = "lm", formula = y ~ x, 
              col="red", fill="red", fullrange = T, lwd=2) +
  theme_pander() +
  scale_x_continuous() +   
  scale_y_continuous() + 
  ggtitle("Rate of Forgetting\nand Eyes-Closed Beta Power") +
  xlab(expression(paste(alpha, " Vocabulary"))) +
  ylab("Low Beta (13-15 Hz) Power Over P8") +
  geom_text(data=survivors, col="red",
            mapping=aes(x=0.25, y=10.5, 
                        label= paste("r =", round(r, 2)))) +
  theme(plot.title = element_text(hjust = 0.5))

ggMarginal(p, col = "white", fill = "black", alpha = 0.5,
           type = "hist", bins = 13)

Eyes-Open EEG Data

(Optional) Preprocess the Data

Set the process_raw variable to TRUE to reprocess the raw EEG data. That might take a very long time.

process_raw = F
if (process_raw) {
  setwd("eyes_open/")
  for (sub in dir(grep("A[1-9]", dir()))) {
    setwd(sub)
    analyze.logfile(sub, "open")
    setwd("..")
  }
  setwd("..")
}

Load the Eyes-Open Spectra and Summary Files

As in the case of eyes-closed data, we are going to examine the spectral and IAF characteristics of eyes-open recordings though the summary files produced by preprocessing.

eo_spectra <- NULL
for (sub in dir("data/eyes_open/")[grep("A[1-9]", 
                                        dir("data/eyes_open/"))]) {
  table <- read_tsv(paste("data/eyes_open/", sub, "/", 
                          sub, "_open_spectra.txt", sep=""),
                    col_types = cols())
  if (is.null(eo_spectra)) {
    eo_spectra <- table
  } else {
    eo_spectra <- eo_spectra %>% bind_rows(table)
  }
}

eo_summary <- NULL
for (sub in dir("data/eyes_open/")[grep("A[1-9]", 
                                        dir("data/eyes_open/"))]) {
  table <- read_tsv(paste("data/eyes_open/", sub, "/", 
                          sub, "_open_summary.txt", sep=""),
                    col_types = cols())
  if (is.null(eo_summary)) {
    eo_summary <- table
  } else {
    eo_summary <- eo_summary %>% bind_rows(table)
  }
}

Individual Alpha frquency

Since eyes-open recordings are somewhat less common, we need to run a few sanity checks on them. The first and most obsvious concerns the IAF, and whether the IAFs during eyes-open recordings are similar and correlated to those observed during eyes-closed sessions.

eo_iafs <- eo_summary %>%
  select(c("Subject", iaf_cols)) %>%
  filter(Subject %in% wbehav$Subject) %>%
  pivot_longer(cols = iaf_cols, names_sep="_", 
               names_to = c("Channel", "Discard"), 
               values_to = "IAF_EO") %>%
  select(Subject, Channel, IAF_EO) %>%
  group_by(Subject) %>%
  summarize(IAF_EO = Mode(IAF_EO))
## `summarise()` ungrouping output (override with `.groups` argument)
iafs <- inner_join(eo_iafs, ec_iafs, by="Subject")

The mean IAF thus calculated is 10.33, which is, once more, exactly in the middle of our alpha frequency band.

ggplot(data=eo_iafs, aes(x = IAF_EO)) +
  geom_histogram(aes(col="white"), fill="black", 
                 colour="white", alpha=0.5, 
                 position="identity", binwidth = 0.5) +
  ggtitle("IAF Distribution, Eyes-Open") + 
  xlab("IAF (Eyes Open)") +
  theme_pander()

As it can be seen, there is a significant correlation in the IAFs between the two recordings (p = 10^{-6}). Between recordings, the individual IAF remains the same +/- 0.83.

ggplot(iafs, aes(x=IAF_EO, y=IAF_EC)) +
  geom_count(alpha=0.5, col="black") + 
  geom_smooth(method = "lm", formula = y ~ x, 
              col="red", fill="red", fullrange = T, lwd=2) +
  xlab("IAF Eyes Open (Hz)") +
  ylab("IAF Eyes Closed (Hz") +
  geom_text(data = summarize(iafs, Mean=mean(IAF_EC)),  # Avoid label overlaps
            x= 9.5, y=11.5, 
            col="red", 
            label=paste("r =", 
                        round(cor(iafs$IAF_EC, iafs$IAF_EO), 2))) +
  ggtitle("Correlation Between Eyes-Closed and Eyes-Open IAF") +
  theme_pander()

Average Spectrum

We can also investigate whether the average spectrum is comparable to that of eyes-closed recordings. To do so, we will calculate the average spectrum across channels, much in the same ways as it was done for eyes-closed data:

l_eo_spectra <- pivot_longer(eo_spectra, cols=names(ec_spectra)[3:130], 
                         names_to="Freq")

l_eo_spectra <- l_eo_spectra %>% 
  rename(Power = value) %>%
  add_column(Recording = "Eyes Open")

l_eo_spectra$Frequency <- as.numeric(substr(l_eo_spectra$Freq, 
                                            0, str_length(l_eo_spectra$Freq) -2))
l_eo_spectra <- l_eo_spectra %>% 
  add_column(Band="Delta", BandMin=0, BandMax=4) 
l_eo_spectra$Band[l_eo_spectra$Frequency <= 40] <- "Gamma"
l_eo_spectra$Band[l_eo_spectra$Frequency < 30] <- "High Beta"
l_eo_spectra$Band[l_eo_spectra$Frequency < 18] <- "Upper Beta"
l_eo_spectra$Band[l_eo_spectra$Frequency < 15] <- "Low Beta"
l_eo_spectra$Band[l_eo_spectra$Frequency < 13] <- "Alpha"
l_eo_spectra$Band[l_eo_spectra$Frequency < 8] <- "Theta"
l_eo_spectra$Band[l_eo_spectra$Frequency < 4] <- "Delta"

l_eo_spectra$BandMin[l_eo_spectra$Frequency <= 40] <- 30
l_eo_spectra$BandMin[l_eo_spectra$Frequency < 30] <- 18
l_eo_spectra$BandMin[l_eo_spectra$Frequency < 18] <- 15
l_eo_spectra$BandMin[l_eo_spectra$Frequency < 15] <- 13
l_eo_spectra$BandMin[l_eo_spectra$Frequency < 13] <- 8
l_eo_spectra$BandMin[l_eo_spectra$Frequency < 8] <- 4
l_eo_spectra$BandMin[l_eo_spectra$Frequency < 4] <- 0

l_eo_spectra$BandMax[l_eo_spectra$Frequency <= 40] <- 40
l_eo_spectra$BandMax[l_eo_spectra$Frequency < 30] <- 30
l_eo_spectra$BandMax[l_eo_spectra$Frequency < 18] <- 18
l_eo_spectra$BandMax[l_eo_spectra$Frequency < 15] <- 15
l_eo_spectra$BandMax[l_eo_spectra$Frequency < 13] <- 13
l_eo_spectra$BandMax[l_eo_spectra$Frequency < 8] <- 8
l_eo_spectra$BandMax[l_eo_spectra$Frequency < 4] <- 4

l_eo_spectra$Band <- factor(l_eo_spectra$Band, 
                        levels = c("Delta", "Theta", "Alpha", 
                                   "Low Beta", "Upper Beta",
                                   "High Beta", "Gamma"))

Now, we remove the three participants for which we have poor quality data

l_eo_spectra <- l_eo_spectra %>%
  filter(Subject %in% behav$Subject)

And we can visualize the eyes-open power spectra by channel:

gd <- l_eo_spectra %>% 
        group_by(Band) %>% 
        summarise(
          Min = mean(BandMin),
          Max = mean(BandMax),
          Power =mean(Power),
          Frequency = mean(BandMin)
        )
## `summarise()` ungrouping output (override with `.groups` argument)
ggplot(data=l_eo_spectra, aes(x=Frequency, y=Power, Channel)) +
  geom_rect(data = gd, aes(xmin = Min, xmax = Max, fill = Band), 
            ymin=0, ymax=Inf, colour=NA, alpha=0.5) +
  stat_summary(fun.data=mean_sdl, 
               geom = "ribbon", colour = "white", alpha = 0.4) +
  stat_summary(fun = mean, geom = "line", lwd = 1) +
  facet_wrap(~ Channel, ncol=4) +
  scale_alpha_manual(values = seq(0.1, 0.9, 0.1)) +
  ggtitle("Eyes-Open Power Spectrum Across Channels") +
  ylab("Log Power") + 
  xlab("Frequency (Hz)") + 
  theme_pander() +
  coord_cartesian(xlim=c(1,40), ylim=c(5, 17)) + #ylim=c(5,17)) +
  scale_fill_brewer(palette = "Set3") +
  theme(plot.title = element_text(hjust = 0.5))

At a first sight, the eyes-open power spectrum looks remarkably similar, with the obvious (and expected) difference of a less prominent pean in the alpha band. To better compare the two types of recordings, we can visualize the avearage spectra on top of ech other:

l_spectra <- rbind(l_ec_spectra, l_eo_spectra)

al_spectra <- l_spectra %>%
  group_by(Subject, Frequency, Band, Recording) %>%
  summarise(Power = mean(Power))
## `summarise()` regrouping output by 'Subject', 'Frequency', 'Band' (override with `.groups` argument)
al_spectra <- al_spectra %>% ungroup()

ggplot(data=al_spectra, aes(x = Frequency, y = Power, 
                            col = Recording, fill = Recording)) +
  annotate("rect", xmin = 0, xmax = 4, ymin = 0, ymax = Inf, 
           alpha = 0.5, fill=K[1]) +
  annotate("rect", xmin = 4, xmax = 8, ymin = 0, ymax = Inf, 
           alpha = 0.5, fill=K[2]) +
  annotate("rect", xmin = 8, xmax = 13, ymin = 0, ymax = Inf, 
           alpha = 0.5, fill=K[3]) +      
  annotate("rect", xmin = 13, xmax = 15, ymin = 0, ymax = Inf, 
           alpha = 0.5, fill=K[4]) +
  annotate("rect", xmin = 15, xmax = 18, ymin = 0, ymax = Inf, 
           alpha = 0.5, fill = K[5]) +
  annotate("rect", xmin = 18, xmax = 30, ymin = 0, ymax = Inf, 
           alpha = 0.5, fill=K[6]) +
  annotate("rect", xmin = 30, xmax = 40, ymin = 0, ymax = Inf,
           alpha = 0.5, fill=K[7]) +
  stat_summary(fun.data = mean_sdl, geom = "ribbon", 
               alpha = 0.5, col = "white") +
  scale_color_brewer(palette = "Set1") +
  scale_fill_brewer(palette = "Set1") +
  stat_summary(fun = mean, geom = "line", lwd = 2) +
  coord_cartesian(xlim=c(0,40), ylim=c(5,18)) +
  xlab("Frequency (Hz)") +
  ylab("Log Power") +
  theme_pander() +
  annotate("text", x=2, y=18, label="Delta", angle=90, hjust=1) +
  annotate("text", x=6, y=18, label="Theta", angle=90, hjust=1) +
  annotate("text", x=10.5, y=18, label="Alpha", angle=90, hjust=1) +
  annotate("text", x=14, y=18, label="Low Beta", angle=90, hjust=1) +
  annotate("text", x=16.5, y=18, label="Upper Beta", angle=90, hjust=1) +
  annotate("text", x=24, y=18, label="High Beta", angle=90, hjust=1) +
  annotate("text", x=35, y=18, label="Gamma", angle=90, hjust=1)

Correlations with Rate of Forgetting

Like we did for eyes-closed data, we can now calculate the correlations between eyes-open EEG power spectra and the behavioral rate fo forgetting for verbal and visual materials.

wbehav <- wbehav %>%
  mutate(GlobalAlpha=(Vocabulary + Maps) / 2)

Adata_eo <- l_eo_spectra %>% 
  group_by(Subject, Channel, Band, Recording) %>% 
  summarize(Power=mean(Power))
## `summarise()` regrouping output by 'Subject', 'Channel', 'Band' (override with `.groups` argument)
Fdata_eo <- inner_join(Adata_eo, behav, by = "Subject")

Cdata_eo <- Fdata_eo %>%
  group_by(material, Channel, Band, Recording) %>%
  summarise(r = cor(Power, alpha),
            p = cor.test(Power, alpha)$p.value,
            rob_r = robcor(Power, alpha))
## `summarise()` regrouping output by 'material', 'Channel', 'Band' (override with `.groups` argument)
Rdata_eo <- Cdata_eo %>%
  group_by(material, Band, Recording) %>%
  mutate(q = p.adjust(p, method="BH")) %>%
  mutate(rob_p = r2p(rob_r, n=50)) %>%
  mutate(rob_q = p.adjust(rob_p, method="BH"))

We save the data so that it can be visualized as a topomap with Python MNE. Here is the full table of statistics:

write_csv(Rdata_eo, "correlations_channel_band_eyes_open.csv", col_names = T)

Rdata_eo %>%
  xtable() %>%
  kable(digits = 3) %>%
  kable_styling(bootstrap_options = c("striped", "hover"))
material Channel Band Recording r p rob_r q rob_p rob_q
Maps AF3 Delta Eyes Open 0.180 0.211 0.111 0.686 0.442 0.998
Maps AF3 Theta Eyes Open 0.122 0.397 0.097 0.556 0.501 0.842
Maps AF3 Alpha Eyes Open 0.218 0.129 0.145 0.200 0.316 0.492
Maps AF3 Low Beta Eyes Open 0.255 0.074 0.249 0.206 0.082 0.246
Maps AF3 Upper Beta Eyes Open 0.383 0.006 0.389 0.021 0.005 0.029
Maps AF3 High Beta Eyes Open 0.279 0.050 0.336 0.140 0.017 0.059
Maps AF3 Gamma Eyes Open 0.236 0.100 0.287 0.447 0.043 0.203
Maps AF4 Delta Eyes Open 0.141 0.330 0.098 0.686 0.500 0.998
Maps AF4 Theta Eyes Open 0.136 0.347 0.158 0.540 0.273 0.842
Maps AF4 Alpha Eyes Open 0.247 0.083 0.185 0.184 0.197 0.391
Maps AF4 Low Beta Eyes Open 0.301 0.034 0.273 0.206 0.055 0.246
Maps AF4 Upper Beta Eyes Open 0.383 0.006 0.403 0.021 0.004 0.029
Maps AF4 High Beta Eyes Open 0.315 0.026 0.417 0.140 0.003 0.036
Maps AF4 Gamma Eyes Open 0.256 0.073 0.300 0.447 0.034 0.203
Maps F3 Delta Eyes Open 0.065 0.656 -0.181 0.707 0.207 0.968
Maps F3 Theta Eyes Open 0.246 0.085 0.011 0.441 0.940 0.975
Maps F3 Alpha Eyes Open 0.232 0.105 0.111 0.184 0.443 0.621
Maps F3 Low Beta Eyes Open 0.221 0.122 0.133 0.244 0.357 0.412
Maps F3 Upper Beta Eyes Open 0.326 0.021 0.292 0.037 0.040 0.070
Maps F3 High Beta Eyes Open 0.219 0.126 0.137 0.253 0.344 0.438
Maps F3 Gamma Eyes Open 0.126 0.384 0.099 0.662 0.495 0.693
Maps F4 Delta Eyes Open 0.103 0.478 -0.044 0.686 0.763 0.998
Maps F4 Theta Eyes Open 0.236 0.099 0.180 0.441 0.212 0.842
Maps F4 Alpha Eyes Open 0.248 0.082 0.206 0.184 0.151 0.352
Maps F4 Low Beta Eyes Open 0.265 0.063 0.235 0.206 0.101 0.246
Maps F4 Upper Beta Eyes Open 0.338 0.016 0.338 0.034 0.016 0.038
Maps F4 High Beta Eyes Open 0.294 0.038 0.355 0.140 0.011 0.053
Maps F4 Gamma Eyes Open 0.204 0.154 0.191 0.447 0.184 0.608
Maps F7 Delta Eyes Open 0.233 0.104 0.144 0.686 0.319 0.998
Maps F7 Theta Eyes Open 0.148 0.304 0.052 0.540 0.722 0.842
Maps F7 Alpha Eyes Open 0.247 0.084 0.175 0.184 0.224 0.391
Maps F7 Low Beta Eyes Open 0.281 0.048 0.151 0.206 0.296 0.391
Maps F7 Upper Beta Eyes Open 0.428 0.002 0.357 0.013 0.011 0.030
Maps F7 High Beta Eyes Open 0.279 0.050 0.190 0.140 0.186 0.371
Maps F7 Gamma Eyes Open 0.202 0.160 0.119 0.447 0.411 0.693
Maps F8 Delta Eyes Open 0.071 0.624 0.030 0.707 0.834 0.998
Maps F8 Theta Eyes Open 0.175 0.225 0.062 0.526 0.668 0.842
Maps F8 Alpha Eyes Open 0.287 0.043 0.241 0.184 0.091 0.352
Maps F8 Low Beta Eyes Open 0.242 0.091 0.240 0.212 0.093 0.246
Maps F8 Upper Beta Eyes Open 0.336 0.017 0.317 0.034 0.025 0.050
Maps F8 High Beta Eyes Open 0.199 0.166 0.178 0.291 0.217 0.380
Maps F8 Gamma Eyes Open 0.088 0.544 0.012 0.662 0.932 0.932
Maps FC5 Delta Eyes Open 0.032 0.826 0.094 0.826 0.517 0.998
Maps FC5 Theta Eyes Open -0.028 0.845 0.005 0.985 0.975 0.975
Maps FC5 Alpha Eyes Open 0.167 0.247 0.057 0.315 0.693 0.693
Maps FC5 Low Beta Eyes Open 0.189 0.188 0.147 0.263 0.307 0.391
Maps FC5 Upper Beta Eyes Open 0.229 0.109 0.245 0.153 0.087 0.110
Maps FC5 High Beta Eyes Open 0.137 0.343 0.054 0.403 0.710 0.710
Maps FC5 Gamma Eyes Open 0.094 0.515 -0.072 0.662 0.621 0.724
Maps FC6 Delta Eyes Open -0.115 0.425 -0.281 0.686 0.048 0.599
Maps FC6 Theta Eyes Open 0.094 0.515 -0.073 0.655 0.614 0.842
Maps FC6 Alpha Eyes Open 0.190 0.187 0.216 0.261 0.131 0.352
Maps FC6 Low Beta Eyes Open 0.132 0.362 0.218 0.461 0.128 0.255
Maps FC6 Upper Beta Eyes Open 0.179 0.214 0.268 0.249 0.060 0.093
Maps FC6 High Beta Eyes Open 0.136 0.346 0.148 0.403 0.303 0.438
Maps FC6 Gamma Eyes Open 0.037 0.798 0.012 0.798 0.932 0.932
Maps O1 Delta Eyes Open 0.074 0.608 -0.014 0.707 0.920 0.998
Maps O1 Theta Eyes Open 0.011 0.938 -0.106 0.988 0.465 0.842
Maps O1 Alpha Eyes Open 0.085 0.556 0.081 0.649 0.577 0.693
Maps O1 Low Beta Eyes Open 0.026 0.857 -0.126 0.857 0.383 0.412
Maps O1 Upper Beta Eyes Open 0.191 0.183 0.193 0.233 0.180 0.194
Maps O1 High Beta Eyes Open 0.145 0.314 0.107 0.403 0.458 0.524
Maps O1 Gamma Eyes Open 0.126 0.383 0.100 0.662 0.492 0.693
Maps O2 Delta Eyes Open 0.123 0.395 0.017 0.686 0.908 0.998
Maps O2 Theta Eyes Open 0.137 0.342 0.057 0.540 0.697 0.842
Maps O2 Alpha Eyes Open 0.238 0.096 0.209 0.184 0.146 0.352
Maps O2 Low Beta Eyes Open 0.210 0.144 0.152 0.244 0.293 0.391
Maps O2 Upper Beta Eyes Open 0.344 0.015 0.369 0.034 0.008 0.029
Maps O2 High Beta Eyes Open 0.239 0.094 0.221 0.220 0.123 0.288
Maps O2 Gamma Eyes Open 0.176 0.222 0.162 0.518 0.261 0.608
Maps P7 Delta Eyes Open 0.128 0.374 0.000 0.686 0.998 0.998
Maps P7 Theta Eyes Open -0.002 0.988 -0.101 0.988 0.487 0.842
Maps P7 Alpha Eyes Open 0.068 0.640 0.066 0.689 0.647 0.693
Maps P7 Low Beta Eyes Open 0.041 0.778 -0.051 0.838 0.727 0.727
Maps P7 Upper Beta Eyes Open 0.112 0.440 0.011 0.474 0.941 0.941
Maps P7 High Beta Eyes Open 0.074 0.608 -0.137 0.608 0.343 0.438
Maps P7 Gamma Eyes Open 0.062 0.669 -0.113 0.720 0.434 0.693
Maps P8 Delta Eyes Open 0.117 0.419 -0.068 0.686 0.639 0.998
Maps P8 Theta Eyes Open 0.275 0.053 0.090 0.441 0.534 0.842
Maps P8 Alpha Eyes Open 0.316 0.025 0.236 0.184 0.098 0.352
Maps P8 Low Beta Eyes Open 0.320 0.024 0.265 0.206 0.063 0.246
Maps P8 Upper Beta Eyes Open 0.436 0.002 0.371 0.013 0.008 0.029
Maps P8 High Beta Eyes Open 0.311 0.028 0.232 0.140 0.105 0.288
Maps P8 Gamma Eyes Open 0.237 0.098 0.175 0.447 0.224 0.608
Maps T7 Delta Eyes Open -0.100 0.490 -0.246 0.686 0.086 0.599
Maps T7 Theta Eyes Open -0.191 0.184 -0.354 0.515 0.012 0.164
Maps T7 Alpha Eyes Open -0.033 0.818 -0.074 0.818 0.610 0.693
Maps T7 Low Beta Eyes Open -0.092 0.524 -0.232 0.611 0.105 0.246
Maps T7 Upper Beta Eyes Open -0.072 0.621 -0.262 0.621 0.067 0.093
Maps T7 High Beta Eyes Open -0.137 0.344 -0.371 0.403 0.008 0.053
Maps T7 Gamma Eyes Open -0.105 0.468 -0.320 0.662 0.024 0.203
Maps T8 Delta Eyes Open 0.198 0.168 -0.010 0.686 0.946 0.998
Maps T8 Theta Eyes Open 0.219 0.126 0.147 0.441 0.307 0.842
Maps T8 Alpha Eyes Open 0.270 0.058 0.298 0.184 0.036 0.352
Maps T8 Low Beta Eyes Open 0.203 0.157 0.209 0.244 0.146 0.255
Maps T8 Upper Beta Eyes Open 0.234 0.102 0.239 0.153 0.094 0.110
Maps T8 High Beta Eyes Open 0.081 0.576 0.101 0.608 0.486 0.524
Maps T8 Gamma Eyes Open 0.083 0.567 0.074 0.662 0.608 0.724
Vocabulary AF3 Delta Eyes Open 0.157 0.277 0.060 0.894 0.680 0.809
Vocabulary AF3 Theta Eyes Open 0.042 0.770 0.126 0.953 0.385 0.995
Vocabulary AF3 Alpha Eyes Open 0.176 0.220 0.044 0.343 0.760 0.819
Vocabulary AF3 Low Beta Eyes Open 0.194 0.177 0.183 0.394 0.202 0.883
Vocabulary AF3 Upper Beta Eyes Open 0.218 0.128 0.192 0.358 0.182 0.851
Vocabulary AF3 High Beta Eyes Open 0.130 0.370 0.196 0.991 0.173 0.806
Vocabulary AF3 Gamma Eyes Open 0.080 0.583 0.134 0.720 0.352 0.603
Vocabulary AF4 Delta Eyes Open 0.090 0.536 -0.021 0.894 0.882 0.882
Vocabulary AF4 Theta Eyes Open 0.062 0.666 0.170 0.953 0.238 0.995
Vocabulary AF4 Alpha Eyes Open 0.196 0.173 0.047 0.343 0.744 0.819
Vocabulary AF4 Low Beta Eyes Open 0.267 0.061 0.219 0.282 0.126 0.883
Vocabulary AF4 Upper Beta Eyes Open 0.253 0.077 0.201 0.269 0.161 0.851
Vocabulary AF4 High Beta Eyes Open 0.139 0.334 0.147 0.991 0.308 0.862
Vocabulary AF4 Gamma Eyes Open 0.079 0.586 0.034 0.720 0.813 0.813
Vocabulary F3 Delta Eyes Open -0.136 0.346 -0.218 0.894 0.128 0.547
Vocabulary F3 Theta Eyes Open 0.042 0.772 0.050 0.953 0.730 0.995
Vocabulary F3 Alpha Eyes Open 0.165 0.253 0.011 0.354 0.941 0.941
Vocabulary F3 Low Beta Eyes Open 0.087 0.549 -0.029 0.641 0.843 0.963
Vocabulary F3 Upper Beta Eyes Open 0.182 0.206 0.039 0.380 0.790 0.942
Vocabulary F3 High Beta Eyes Open -0.002 0.991 -0.129 0.991 0.372 0.868
Vocabulary F3 Gamma Eyes Open -0.096 0.509 -0.153 0.720 0.288 0.603
Vocabulary F4 Delta Eyes Open -0.122 0.398 -0.219 0.894 0.127 0.547
Vocabulary F4 Theta Eyes Open 0.043 0.768 0.119 0.953 0.411 0.995
Vocabulary F4 Alpha Eyes Open 0.177 0.218 0.058 0.343 0.690 0.819
Vocabulary F4 Low Beta Eyes Open 0.176 0.222 -0.017 0.394 0.907 0.963
Vocabulary F4 Upper Beta Eyes Open 0.201 0.163 0.025 0.379 0.865 0.942
Vocabulary F4 High Beta Eyes Open 0.010 0.946 0.030 0.991 0.834 0.919
Vocabulary F4 Gamma Eyes Open -0.114 0.430 -0.173 0.720 0.230 0.603
Vocabulary F7 Delta Eyes Open 0.156 0.279 0.057 0.894 0.693 0.809
Vocabulary F7 Theta Eyes Open 0.087 0.550 0.201 0.953 0.161 0.995
Vocabulary F7 Alpha Eyes Open 0.188 0.192 0.081 0.343 0.574 0.819
Vocabulary F7 Low Beta Eyes Open 0.215 0.133 0.111 0.394 0.444 0.888
Vocabulary F7 Upper Beta Eyes Open 0.258 0.070 0.111 0.269 0.443 0.942
Vocabulary F7 High Beta Eyes Open 0.142 0.325 0.006 0.991 0.968 0.968
Vocabulary F7 Gamma Eyes Open 0.072 0.617 -0.101 0.720 0.487 0.603
Vocabulary F8 Delta Eyes Open -0.050 0.729 -0.029 0.894 0.840 0.882
Vocabulary F8 Theta Eyes Open 0.001 0.995 0.042 0.995 0.773 0.995
Vocabulary F8 Alpha Eyes Open 0.208 0.148 0.102 0.343 0.481 0.819
Vocabulary F8 Low Beta Eyes Open 0.175 0.225 0.090 0.394 0.536 0.899
Vocabulary F8 Upper Beta Eyes Open 0.178 0.217 0.028 0.380 0.846 0.942
Vocabulary F8 High Beta Eyes Open 0.013 0.928 0.085 0.991 0.555 0.919
Vocabulary F8 Gamma Eyes Open -0.104 0.473 -0.096 0.720 0.506 0.603
Vocabulary FC5 Delta Eyes Open -0.073 0.617 -0.204 0.894 0.156 0.547
Vocabulary FC5 Theta Eyes Open -0.172 0.233 -0.092 0.953 0.525 0.995
Vocabulary FC5 Alpha Eyes Open 0.063 0.664 -0.126 0.721 0.384 0.819
Vocabulary FC5 Low Beta Eyes Open 0.049 0.737 0.021 0.737 0.885 0.963
Vocabulary FC5 Upper Beta Eyes Open 0.085 0.559 0.023 0.711 0.875 0.942
Vocabulary FC5 High Beta Eyes Open 0.006 0.970 -0.027 0.991 0.853 0.919
Vocabulary FC5 Gamma Eyes Open -0.019 0.897 -0.094 0.897 0.517 0.603
Vocabulary FC6 Delta Eyes Open -0.166 0.248 -0.224 0.894 0.118 0.547
Vocabulary FC6 Theta Eyes Open -0.037 0.799 -0.077 0.953 0.596 0.995
Vocabulary FC6 Alpha Eyes Open 0.110 0.446 0.061 0.568 0.672 0.819
Vocabulary FC6 Low Beta Eyes Open 0.109 0.450 0.159 0.610 0.269 0.883
Vocabulary FC6 Upper Beta Eyes Open 0.054 0.710 0.062 0.764 0.669 0.942
Vocabulary FC6 High Beta Eyes Open -0.018 0.902 0.028 0.991 0.845 0.919
Vocabulary FC6 Gamma Eyes Open -0.101 0.485 -0.123 0.720 0.395 0.603
Vocabulary O1 Delta Eyes Open -0.096 0.506 -0.117 0.894 0.419 0.653
Vocabulary O1 Theta Eyes Open -0.049 0.734 -0.002 0.953 0.987 0.995
Vocabulary O1 Alpha Eyes Open 0.185 0.198 0.044 0.343 0.760 0.819
Vocabulary O1 Low Beta Eyes Open 0.102 0.480 -0.081 0.610 0.578 0.899
Vocabulary O1 Upper Beta Eyes Open 0.163 0.258 -0.043 0.401 0.767 0.942
Vocabulary O1 High Beta Eyes Open -0.033 0.818 -0.164 0.991 0.254 0.862
Vocabulary O1 Gamma Eyes Open -0.108 0.457 -0.179 0.720 0.214 0.603
Vocabulary O2 Delta Eyes Open -0.043 0.766 -0.124 0.894 0.390 0.653
Vocabulary O2 Theta Eyes Open 0.026 0.859 0.045 0.953 0.755 0.995
Vocabulary O2 Alpha Eyes Open 0.242 0.090 0.109 0.343 0.451 0.819
Vocabulary O2 Low Beta Eyes Open 0.280 0.049 0.008 0.282 0.954 0.963
Vocabulary O2 Upper Beta Eyes Open 0.293 0.039 0.086 0.269 0.553 0.942
Vocabulary O2 High Beta Eyes Open 0.058 0.692 -0.079 0.991 0.588 0.919
Vocabulary O2 Gamma Eyes Open -0.081 0.574 -0.142 0.720 0.327 0.603
Vocabulary P7 Delta Eyes Open -0.123 0.395 -0.105 0.894 0.466 0.653
Vocabulary P7 Theta Eyes Open -0.171 0.234 0.001 0.953 0.992 0.995
Vocabulary P7 Alpha Eyes Open 0.062 0.670 0.047 0.721 0.745 0.819
Vocabulary P7 Low Beta Eyes Open -0.054 0.712 -0.147 0.737 0.307 0.883
Vocabulary P7 Upper Beta Eyes Open 0.001 0.994 -0.159 0.994 0.269 0.941
Vocabulary P7 High Beta Eyes Open -0.127 0.378 -0.269 0.991 0.059 0.806
Vocabulary P7 Gamma Eyes Open -0.155 0.281 -0.281 0.720 0.048 0.603
Vocabulary P8 Delta Eyes Open -0.067 0.646 -0.172 0.894 0.232 0.651
Vocabulary P8 Theta Eyes Open 0.100 0.491 -0.001 0.953 0.995 0.995
Vocabulary P8 Alpha Eyes Open 0.241 0.092 0.130 0.343 0.369 0.819
Vocabulary P8 Low Beta Eyes Open 0.296 0.037 0.127 0.282 0.379 0.883
Vocabulary P8 Upper Beta Eyes Open 0.313 0.027 0.130 0.269 0.368 0.942
Vocabulary P8 High Beta Eyes Open 0.082 0.574 -0.047 0.991 0.748 0.919
Vocabulary P8 Gamma Eyes Open -0.049 0.736 -0.180 0.793 0.212 0.603
Vocabulary T7 Delta Eyes Open 0.006 0.968 -0.147 0.968 0.308 0.653
Vocabulary T7 Theta Eyes Open -0.202 0.160 -0.186 0.953 0.196 0.995
Vocabulary T7 Alpha Eyes Open 0.012 0.935 -0.113 0.935 0.435 0.819
Vocabulary T7 Low Beta Eyes Open -0.109 0.450 -0.134 0.610 0.352 0.883
Vocabulary T7 Upper Beta Eyes Open -0.097 0.502 -0.222 0.703 0.121 0.851
Vocabulary T7 High Beta Eyes Open -0.132 0.359 -0.219 0.991 0.126 0.806
Vocabulary T7 Gamma Eyes Open -0.108 0.454 -0.222 0.720 0.121 0.603
Vocabulary T8 Delta Eyes Open 0.006 0.968 -0.113 0.968 0.436 0.653
Vocabulary T8 Theta Eyes Open 0.021 0.885 -0.037 0.953 0.800 0.995
Vocabulary T8 Alpha Eyes Open 0.179 0.213 0.109 0.343 0.451 0.819
Vocabulary T8 Low Beta Eyes Open 0.186 0.196 0.007 0.394 0.963 0.963
Vocabulary T8 Upper Beta Eyes Open 0.057 0.693 -0.001 0.764 0.994 0.994
Vocabulary T8 High Beta Eyes Open -0.098 0.497 -0.068 0.991 0.639 0.919
Vocabulary T8 Gamma Eyes Open -0.103 0.477 -0.072 0.720 0.619 0.667

And here is the corresponding distributions of r and p values. The dashed lines correspond to a significant threshold of p < .05 on either a r or a p-value scale.

ggplot(Rdata_eo, aes(x = Band, y = r, col = Channel)) +
  geom_point() +
  stat_summary(fun.data = "mean_se", col="black", 
               alpha=0.5, geom = "errorbar") +
  facet_wrap(~ material) +
  ggtitle("Correlation, by Band") +
  ylab("r value") +
  annotate("segment", x=-Inf, xend=Inf, y=0.28, yend = 0.28, lty=2) +
  annotate("segment", x=-Inf, xend=Inf, y=-0.28, yend = -0.28, lty=2) +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  theme_pander()

ggplot(Rdata_eo, aes(x = Band, y = p, col = Channel)) +
  geom_point() +
  stat_summary(fun.data = "mean_se", col="black", 
               alpha=0.5, geom = "errorbar") +
  ggtitle("p-value, by Band") +
  ylab("p value") +
  facet_wrap(~ material) +
  annotate("segment", x=-Inf, xend=Inf, y=0.05, yend = 0.05, lty=2) +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  scale_y_log10() +
  theme_pander()

Now, we might wonder how much the correlations change from eyes closed to eyes open recordings. The best way to chack is to visualize then as a scatterplot:

Rdata <- bind_rows(Rdata_ec, Rdata_eo)
wrdata <- pivot_wider(Rdata, id_cols = c("material", "Channel", "Band"),
                      names_from = Recording, 
                      values_from = r)

ggplot(wrdata, aes(x = `Eyes Open`, y = `Eyes Closed`, 
                   col = material)) +
  annotate("segment", x = 0, y=-Inf, xend=0, 
           yend=Inf, col="grey", lwd=1, lty=1) +
  annotate("segment", x = -Inf, y=0, xend=Inf, 
           yend=0, col="grey", lwd=1, lty=1) +
  
  geom_point(alpha=0.5, size=3) +
  annotate("segment", x = -0.25, y=-0.25, xend=0.5, 
           yend=0.5, col="black", lwd=1, lty=2) +
  theme(plot.title = element_text(hjust = 0.5)) +
  #geom_smooth(method = "lm", formula = y ~ x, 
  #            fullrange = T, lwd = 1) +
  scale_color_brewer(palette="Dark2") +
  ggtitle("Correlation Coefficients Across Recordings") +
  theme_pander()

Let’s tabulate only those channels that survive the FDR correction:

survivors <- Rdata_eo %>%
  filter(q < 0.05 | rob_q < 0.05)
  
survivors %>%
  xtable() %>%
  kable(digits = 3) %>%
  kable_styling(bootstrap_options = c("striped", "hover"))
material Channel Band Recording r p rob_r q rob_p rob_q
Maps AF3 Upper Beta Eyes Open 0.383 0.006 0.389 0.021 0.005 0.029
Maps AF4 Upper Beta Eyes Open 0.383 0.006 0.403 0.021 0.004 0.029
Maps AF4 High Beta Eyes Open 0.315 0.026 0.417 0.140 0.003 0.036
Maps F3 Upper Beta Eyes Open 0.326 0.021 0.292 0.037 0.040 0.070
Maps F4 Upper Beta Eyes Open 0.338 0.016 0.338 0.034 0.016 0.038
Maps F7 Upper Beta Eyes Open 0.428 0.002 0.357 0.013 0.011 0.030
Maps F8 Upper Beta Eyes Open 0.336 0.017 0.317 0.034 0.025 0.050
Maps O2 Upper Beta Eyes Open 0.344 0.015 0.369 0.034 0.008 0.029
Maps P8 Upper Beta Eyes Open 0.436 0.002 0.371 0.013 0.008 0.029

In the case of eyes-open data, we have a much larger set of channels that survive correction for multiple comparison. Although these correlations generally reflect the same trends we have seen the eyes-closed data (i.e., significant positive correlations for prefrontal and right parietal sites), they are now stroger for visual (not verbal) materials and centered at at slightly higher frequency (upper beta instead of low beta).

Here is an overview of the scatterplots and correlations:

focus <- Fdata_eo %>%
  filter(material == "Maps", 
         Channel %in% survivors$Channel,
         Band == "Upper Beta") %>%
  rename(Alpha = alpha)

ggplot(focus, aes(x=Alpha, y=Power)) +
  geom_point(size=4, alpha=0.5, col="black") + 
  geom_smooth(method = "lm", formula = y ~ x, 
              col="red", fill="red", fullrange = T, lwd=2) +
  theme_pander() +
  scale_x_continuous() +   
  scale_y_continuous() + 
  ggtitle("Rate of Forgetting and Eyes-Open Beta Power") +
  xlab(expression(paste(alpha, " Maps"))) +
  ylab("Upper Beta Power (15-18 Hz)") +
  facet_wrap(~ Channel, scales="free_y") +
  geom_text(data=survivors, col="red",
            mapping=aes(x=0.25, y=9.5, 
                        label= paste("r =", round(r, 2)))) +
  theme(panel.spacing = unit(1.5, "lines")) +
  theme(plot.title = element_text(hjust = 0.5))

Predicting Rate of Forgetting with Group Lasso

So far, we have shown that neurophysiological signals exists that are correlated with the rate of forgetting. This, however, does not directly answer wheter we could “read” an individual’s rate of forgetting from their EEG data directy.

Group LASSO

To do so, we need to use a ML approach. Specifically, here we will use group LASSO regression. Group LASSO is a way to combine regression, validation, and feature selection into a single approach.

LASSO works like a normal regression, with the additional constraint that the \(\beta\) regressors need to minimize the sum of the residual sum of squares (RSS) and the quantity \(- \lambda||\beta||_{1}\), where \(||\beta||_{1}\) is the first-order norm (the sum of absolute values of each regressor weight). For \(\lambda = 0\), LASSO reduces to normal regression but, as the value of \(\lambda\) grows, more and more regressors are “pushed” to zero and removed from the pool. In group LASSO, regressors are combined and selected by groups, which is a natural choice when natural groupings exists, as in the cases of frequency bands.

As a demo, we will pilot this approach to eyes-closed recordings and the combined rates of forgetting.an

Data Preparation

First, we need to transform the data appropriately, converting from the long to the wide format, which is better suited for regression:

library(gglasso)
wfdata <- Fdata_ec %>% 
  pivot_wider(id_cols = c("Subject", "Channel", 
                          "Band", "material", "alpha"), 
              names_from = c("Channel", "Band"), 
              values_from = c("Power"))

wide_data_ec <- wfdata %>%
  pivot_wider(names_from = c("material"), 
              values_from = "alpha")

From the wide format data, we are going to define the data that will enter the regression, the matrix of observations X and the vector of variables Y. The matrix of observations X is 50 x 98 matrix, corresponding to 50 participants x 98 possible power values (14 channels x 7 frequency bands). The Y vector is made of 50 observed rates of forgetting. To make the prediction reliable, we will average the rates of forgetting across materials (Maps + Vocabulary)

channel_names <- c("AF3", "AF4", "F3", "F4", 
                   "F7", "F8", "FC5", "FC6", 
                   "T7", "T8", "P7", "P8", 
                   "O1", "O2")


band_names <- c("Delta", "Theta", "Alpha", "Low Beta", 
                "Upper Beta", "High Beta", "Gamma")

by_band_order <- as.vector(
  outer(channel_names, 
        band_names, 
        function(x, y){
          paste(x, y, sep="_")
          }))

# Predictors
X <- wide_data_ec[,c(-1, -100, -101)] %>%
  #select(ends_with("Beta")) %>%
  as.matrix()

X <- X[,by_band_order]
# We need to reorder X by frequency bands


# Maps
Ymaps <- wide_data_ec[,c(101)] %>%
  as.matrix()

# Vocab
Yvoc <- wide_data_ec[,c(101)] %>%
  as.matrix()

# Average across materials to obrtain stable estimates
Y <- (Ymaps + Yvoc)/2

# Let's save the mean (will be halpful later)
uY <- mean(Y)

# Center Y to remove dominant effect of intercept
Y <- Y - uY

Finally, we need to define our set of grouping variables, defined as a vector of numbers that identify each group. We are going to create two such vectors, one for the freqency bands and one for the channels. In this example we are going to use bands as the grouping variables.

bands <- rep(1:7, each=14)
channels <- sort(rep(1:14, 7))

Fitting the LASSO

Now, with that in place, we can fit the LASSO model. The LASSO model is fit much like a normal regression, with an additional partameter \(\lambda\).

Because we do not know a priori which value of \(lambda\) to pick, the canonical solution is to fit fit different models for different values of \(\lambda\).

fit <- gglasso(x = X, y = Y, 
               group = bands,
               loss = 'ls', 
               nlambda=100,
               lambda.factor = 0.001)
coef.mat=fit$beta

Finding the optimal \(\lambda\) with Cross-Validation

Our goal, of course, is generalizability across participants. Although the fit model is important, what we really care is a different measure, that of cross-validation. For cross-validation, we are going to use the n-fold approach, in which the data is randomly split so that 1/n of it is saved for test. (if n is identical to the number of participants, it becomes the “Leave-One-Out” validation scheme). Here, we used the Leave-One-Out method, which guarantees that the results are the same every time this script is ruin (because there only one possible permutation of the data). So, n = 50.

fit.cv <- cv.gglasso(x = X,
                     y = Y,
                     group = bands,
                     pred.loss = "L1",
                     nlambda = 100,
                     lambda.factor = 0.001,
                     nfolds = 50)

Visualizing Validation Results

Here are the fit and cross-validation plots, with the vertical lines marking the points corresponding to \(\lambda_{min}\) (optimal for cross-validation) and
\(\lambda_{1SE}\) (more conservative model). Because we have used the Leave-One-Out validation scheme, we are can use the the more aggressive \(\lambda_{min}\) estimate, since our sample of the folds was exhaustive.

# Best lambda

lmin <- fit.cv$lambda.min  # Optimal lambda, maximizes generalization
l1se <- fit.cv$lambda.1se  # Conservative model, min + 1SE

plot(fit.cv, 
     pch=20,
     lwd=2)

plot(fit, group=T, 
     col = inferno(length(unique(fit$group)) + 1), 
     lwd = 2)

legend(x="topright", 
       legend=c("Delta", "Theta", "Alpha",
                "Low Beta", "Upper Beta", "High Beta",
                "Gamma"),
       bty="n",
       ncol=2,
       col=inferno(length(unique(fit$group)) + 1),
       lty=1, lwd=2)
abline(v=log(lmin), lty=2)
abline(v=log(l1se), lty=2)

Using the Lambda min value, we can now compare predicted vs. observed values.

prediction <- predict(object = fit,
                    newx = X,
                    s = lmin,
                    type='link')

observed <- data.frame(Subject = wide_data_ec$Subject,
                       RoF = as_vector(Y) + uY,
                       Condition = "Observed") %>%
  rename(RoF = Maps)

predicted <- data.frame(Subject = wide_data_ec$Subject,
                       RoF = as_vector(prediction) + uY,
                       Condition = "Predicted") %>%
  rename(RoF = X1)

comparison <- as_tibble(rbind(observed, predicted))

plt = cbind(Y,
            predict(object = fit,
                    newx = X,
                    s = lmin,
                    type='link'))

# matplot(plt,
#         main="Predicted vs Actual",
#         type='b',
#         lwd=2,
#         pch="o",
#         col=viridis(3),
#         xlab="Subject",
#         ylab="Rate of Forgetting (alpha)")

ggplot(comparison, aes(x=Subject, y=RoF), col=Condition) +
  geom_point(aes(col=Condition)) +
  geom_line(alpha=0.5, lty=2) +
  annotate("text", x= 40, y = 0.20, 
           label=(paste("r =", 
                        round(cor(Y, prediction),
                              2)))) +
  theme_pander() +
  ylab("Rate of Forgetting")+
  ggtitle("Cross-Validation:\nPredicted vs. Observed Rates of Forgetting") +
  theme(axis.text.x = element_text(angle = 90, hjust = 1, size = 6)) 

wcomparison <- comparison %>%
  pivot_wider(names_from=Condition, values_from = RoF)

p <- ggplot(wcomparison, aes(x = Predicted, y = Observed)) +
  geom_point(alpha=0.5, size=4) +
  geom_abline(slope = 1, intercept = 0,
              lwd=1, col="blue", lty=2) +
  annotate("text", x= 0.40, y = 0.25, 
           label=(paste("r =", 
                        round(cor(Y, prediction),
                              2)))) +
  theme_pander() +
  #coord_fixed() +
  coord_equal(ratio=1) +
  ylab("Rate of Forgetting (Observed)") +
  xlab("Rate of Forgetting (Predicted)") +
  ggtitle("Cross-Validation") 

ggMarginal(p, col="white", fill="black", alpha=0.5,
           type="hist", bins=13)

In terms of overall error, the root mean squared error between predicted and observed Rate of Forgetting is RMSE = 0.024

And now, let’s print the full table of beta regression weights (for inspectio and analysis) at the desiored value of \(\lambda_{min}\). We can also save the weights for future analysis.

get_channel <- function(s) {
  str_split(s, "_", 2)[[1]][1]
}

get_band <- function(s) {
  str_split(s, "_", 2)[[1]][2]
}

vget_channel <- Vectorize(get_channel)
vget_band <- Vectorize(get_band)


coef(fit.cv, 
     s=lmin) -> betas
  
bdf <- data.frame("Predictor" = rownames(betas),
                  "Beta" = as.numeric(betas)) %>%
  mutate(Channel = vget_channel(Predictor),
         Band = vget_band(Predictor)) 

bdf %>%
  filter(Beta != 0) %>%
  xtable() %>%
  kable(digits = 5) %>%
  kable_styling(bootstrap_options = c("striped", "hover"))
Predictor Beta Channel Band
(Intercept) 0.00955 (Intercept) NA
AF3_Delta -0.00659 AF3 Delta
AF4_Delta 0.00294 AF4 Delta
F3_Delta -0.02081 F3 Delta
F4_Delta 0.03104 F4 Delta
F7_Delta 0.01171 F7 Delta
F8_Delta -0.01349 F8 Delta
FC5_Delta -0.01473 FC5 Delta
FC6_Delta -0.01259 FC6 Delta
T7_Delta -0.00654 T7 Delta
T8_Delta 0.01771 T8 Delta
P7_Delta 0.00053 P7 Delta
P8_Delta 0.02433 P8 Delta
O1_Delta 0.00076 O1 Delta
O2_Delta 0.01153 O2 Delta
AF3_Theta -0.00014 AF3 Theta
AF4_Theta -0.00003 AF4 Theta
F3_Theta -0.00103 F3 Theta
F4_Theta -0.00013 F4 Theta
F7_Theta -0.00101 F7 Theta
F8_Theta -0.00092 F8 Theta
FC5_Theta -0.00081 FC5 Theta
FC6_Theta 0.00035 FC6 Theta
T7_Theta -0.00324 T7 Theta
T8_Theta 0.00128 T8 Theta
P7_Theta -0.00182 P7 Theta
P8_Theta 0.00146 P8 Theta
O1_Theta 0.00001 O1 Theta
O2_Theta 0.00095 O2 Theta
AF3_Alpha -0.00175 AF3 Alpha
AF4_Alpha 0.00352 AF4 Alpha
F3_Alpha 0.00034 F3 Alpha
F4_Alpha 0.00289 F4 Alpha
F7_Alpha 0.00115 F7 Alpha
F8_Alpha 0.00520 F8 Alpha
FC5_Alpha 0.00101 FC5 Alpha
FC6_Alpha 0.01122 FC6 Alpha
T7_Alpha -0.00497 T7 Alpha
T8_Alpha 0.01223 T8 Alpha
P7_Alpha -0.01927 P7 Alpha
P8_Alpha -0.00379 P8 Alpha
O1_Alpha -0.00753 O1 Alpha
O2_Alpha 0.00392 O2 Alpha
AF3_Upper Beta 0.00068 AF3 Upper Beta
AF4_Upper Beta 0.00089 AF4 Upper Beta
F3_Upper Beta 0.00009 F3 Upper Beta
F4_Upper Beta 0.00030 F4 Upper Beta
F7_Upper Beta 0.00042 F7 Upper Beta
F8_Upper Beta 0.00064 F8 Upper Beta
FC5_Upper Beta 0.00014 FC5 Upper Beta
FC6_Upper Beta 0.00069 FC6 Upper Beta
T7_Upper Beta 0.00046 T7 Upper Beta
T8_Upper Beta 0.00027 T8 Upper Beta
P7_Upper Beta 0.00023 P7 Upper Beta
P8_Upper Beta 0.00002 P8 Upper Beta
O1_Upper Beta 0.00058 O1 Upper Beta
O2_Upper Beta 0.00066 O2 Upper Beta
AF3_Gamma 0.00144 AF3 Gamma
AF4_Gamma 0.00539 AF4 Gamma
F3_Gamma -0.01068 F3 Gamma
F4_Gamma -0.00540 F4 Gamma
F7_Gamma -0.01039 F7 Gamma
F8_Gamma -0.00435 F8 Gamma
FC5_Gamma -0.00148 FC5 Gamma
FC6_Gamma -0.00273 FC6 Gamma
T7_Gamma 0.00736 T7 Gamma
T8_Gamma -0.01448 T8 Gamma
P7_Gamma -0.00609 P7 Gamma
P8_Gamma -0.00418 P8 Gamma
O1_Gamma 0.00834 O1 Gamma
O2_Gamma 0.01031 O2 Gamma 
write_csv(bdf, "group_lasso_weights.csv", col_names = T)

And here is the visualization of the corresponding weights as a topomap:

Topomap of Beta weights

Topomap of Beta weights